Properties

Label 8015.2.a.l.1.23
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.23
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.883363 q^{2} +2.03323 q^{3} -1.21967 q^{4} -1.00000 q^{5} -1.79608 q^{6} -1.00000 q^{7} +2.84414 q^{8} +1.13404 q^{9} +O(q^{10})\) \(q-0.883363 q^{2} +2.03323 q^{3} -1.21967 q^{4} -1.00000 q^{5} -1.79608 q^{6} -1.00000 q^{7} +2.84414 q^{8} +1.13404 q^{9} +0.883363 q^{10} +6.34675 q^{11} -2.47987 q^{12} +2.46714 q^{13} +0.883363 q^{14} -2.03323 q^{15} -0.0730644 q^{16} -7.94029 q^{17} -1.00177 q^{18} -0.535203 q^{19} +1.21967 q^{20} -2.03323 q^{21} -5.60648 q^{22} -7.18811 q^{23} +5.78280 q^{24} +1.00000 q^{25} -2.17938 q^{26} -3.79393 q^{27} +1.21967 q^{28} +3.71349 q^{29} +1.79608 q^{30} +7.48378 q^{31} -5.62373 q^{32} +12.9044 q^{33} +7.01416 q^{34} +1.00000 q^{35} -1.38316 q^{36} +10.3832 q^{37} +0.472778 q^{38} +5.01627 q^{39} -2.84414 q^{40} -3.56613 q^{41} +1.79608 q^{42} +0.896867 q^{43} -7.74094 q^{44} -1.13404 q^{45} +6.34971 q^{46} +5.81099 q^{47} -0.148557 q^{48} +1.00000 q^{49} -0.883363 q^{50} -16.1445 q^{51} -3.00910 q^{52} +6.83234 q^{53} +3.35142 q^{54} -6.34675 q^{55} -2.84414 q^{56} -1.08819 q^{57} -3.28036 q^{58} -14.7175 q^{59} +2.47987 q^{60} +9.25738 q^{61} -6.61089 q^{62} -1.13404 q^{63} +5.11392 q^{64} -2.46714 q^{65} -11.3993 q^{66} -1.67234 q^{67} +9.68454 q^{68} -14.6151 q^{69} -0.883363 q^{70} -4.43857 q^{71} +3.22537 q^{72} -4.00883 q^{73} -9.17216 q^{74} +2.03323 q^{75} +0.652771 q^{76} -6.34675 q^{77} -4.43119 q^{78} +4.06403 q^{79} +0.0730644 q^{80} -11.1161 q^{81} +3.15019 q^{82} +14.7447 q^{83} +2.47987 q^{84} +7.94029 q^{85} -0.792259 q^{86} +7.55039 q^{87} +18.0510 q^{88} -0.355306 q^{89} +1.00177 q^{90} -2.46714 q^{91} +8.76712 q^{92} +15.2163 q^{93} -5.13321 q^{94} +0.535203 q^{95} -11.4344 q^{96} +16.5587 q^{97} -0.883363 q^{98} +7.19747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.883363 −0.624632 −0.312316 0.949978i \(-0.601105\pi\)
−0.312316 + 0.949978i \(0.601105\pi\)
\(3\) 2.03323 1.17389 0.586944 0.809627i \(-0.300331\pi\)
0.586944 + 0.809627i \(0.300331\pi\)
\(4\) −1.21967 −0.609835
\(5\) −1.00000 −0.447214
\(6\) −1.79608 −0.733248
\(7\) −1.00000 −0.377964
\(8\) 2.84414 1.00555
\(9\) 1.13404 0.378014
\(10\) 0.883363 0.279344
\(11\) 6.34675 1.91362 0.956808 0.290720i \(-0.0938947\pi\)
0.956808 + 0.290720i \(0.0938947\pi\)
\(12\) −2.47987 −0.715878
\(13\) 2.46714 0.684262 0.342131 0.939652i \(-0.388851\pi\)
0.342131 + 0.939652i \(0.388851\pi\)
\(14\) 0.883363 0.236089
\(15\) −2.03323 −0.524979
\(16\) −0.0730644 −0.0182661
\(17\) −7.94029 −1.92580 −0.962902 0.269851i \(-0.913025\pi\)
−0.962902 + 0.269851i \(0.913025\pi\)
\(18\) −1.00177 −0.236119
\(19\) −0.535203 −0.122784 −0.0613920 0.998114i \(-0.519554\pi\)
−0.0613920 + 0.998114i \(0.519554\pi\)
\(20\) 1.21967 0.272727
\(21\) −2.03323 −0.443688
\(22\) −5.60648 −1.19531
\(23\) −7.18811 −1.49882 −0.749412 0.662104i \(-0.769664\pi\)
−0.749412 + 0.662104i \(0.769664\pi\)
\(24\) 5.78280 1.18041
\(25\) 1.00000 0.200000
\(26\) −2.17938 −0.427412
\(27\) −3.79393 −0.730142
\(28\) 1.21967 0.230496
\(29\) 3.71349 0.689577 0.344789 0.938680i \(-0.387951\pi\)
0.344789 + 0.938680i \(0.387951\pi\)
\(30\) 1.79608 0.327918
\(31\) 7.48378 1.34413 0.672063 0.740494i \(-0.265408\pi\)
0.672063 + 0.740494i \(0.265408\pi\)
\(32\) −5.62373 −0.994145
\(33\) 12.9044 2.24637
\(34\) 7.01416 1.20292
\(35\) 1.00000 0.169031
\(36\) −1.38316 −0.230526
\(37\) 10.3832 1.70699 0.853497 0.521098i \(-0.174478\pi\)
0.853497 + 0.521098i \(0.174478\pi\)
\(38\) 0.472778 0.0766947
\(39\) 5.01627 0.803247
\(40\) −2.84414 −0.449698
\(41\) −3.56613 −0.556936 −0.278468 0.960445i \(-0.589827\pi\)
−0.278468 + 0.960445i \(0.589827\pi\)
\(42\) 1.79608 0.277142
\(43\) 0.896867 0.136771 0.0683855 0.997659i \(-0.478215\pi\)
0.0683855 + 0.997659i \(0.478215\pi\)
\(44\) −7.74094 −1.16699
\(45\) −1.13404 −0.169053
\(46\) 6.34971 0.936213
\(47\) 5.81099 0.847620 0.423810 0.905751i \(-0.360693\pi\)
0.423810 + 0.905751i \(0.360693\pi\)
\(48\) −0.148557 −0.0214424
\(49\) 1.00000 0.142857
\(50\) −0.883363 −0.124926
\(51\) −16.1445 −2.26068
\(52\) −3.00910 −0.417287
\(53\) 6.83234 0.938494 0.469247 0.883067i \(-0.344525\pi\)
0.469247 + 0.883067i \(0.344525\pi\)
\(54\) 3.35142 0.456070
\(55\) −6.34675 −0.855795
\(56\) −2.84414 −0.380064
\(57\) −1.08819 −0.144135
\(58\) −3.28036 −0.430732
\(59\) −14.7175 −1.91605 −0.958027 0.286679i \(-0.907449\pi\)
−0.958027 + 0.286679i \(0.907449\pi\)
\(60\) 2.47987 0.320150
\(61\) 9.25738 1.18529 0.592643 0.805465i \(-0.298085\pi\)
0.592643 + 0.805465i \(0.298085\pi\)
\(62\) −6.61089 −0.839584
\(63\) −1.13404 −0.142876
\(64\) 5.11392 0.639240
\(65\) −2.46714 −0.306011
\(66\) −11.3993 −1.40316
\(67\) −1.67234 −0.204309 −0.102155 0.994769i \(-0.532574\pi\)
−0.102155 + 0.994769i \(0.532574\pi\)
\(68\) 9.68454 1.17442
\(69\) −14.6151 −1.75945
\(70\) −0.883363 −0.105582
\(71\) −4.43857 −0.526761 −0.263380 0.964692i \(-0.584837\pi\)
−0.263380 + 0.964692i \(0.584837\pi\)
\(72\) 3.22537 0.380113
\(73\) −4.00883 −0.469198 −0.234599 0.972092i \(-0.575378\pi\)
−0.234599 + 0.972092i \(0.575378\pi\)
\(74\) −9.17216 −1.06624
\(75\) 2.03323 0.234778
\(76\) 0.652771 0.0748779
\(77\) −6.34675 −0.723279
\(78\) −4.43119 −0.501733
\(79\) 4.06403 0.457239 0.228619 0.973516i \(-0.426579\pi\)
0.228619 + 0.973516i \(0.426579\pi\)
\(80\) 0.0730644 0.00816885
\(81\) −11.1161 −1.23512
\(82\) 3.15019 0.347880
\(83\) 14.7447 1.61844 0.809222 0.587503i \(-0.199889\pi\)
0.809222 + 0.587503i \(0.199889\pi\)
\(84\) 2.47987 0.270577
\(85\) 7.94029 0.861246
\(86\) −0.792259 −0.0854315
\(87\) 7.55039 0.809486
\(88\) 18.0510 1.92425
\(89\) −0.355306 −0.0376623 −0.0188312 0.999823i \(-0.505994\pi\)
−0.0188312 + 0.999823i \(0.505994\pi\)
\(90\) 1.00177 0.105596
\(91\) −2.46714 −0.258627
\(92\) 8.76712 0.914035
\(93\) 15.2163 1.57785
\(94\) −5.13321 −0.529450
\(95\) 0.535203 0.0549106
\(96\) −11.4344 −1.16701
\(97\) 16.5587 1.68128 0.840641 0.541593i \(-0.182179\pi\)
0.840641 + 0.541593i \(0.182179\pi\)
\(98\) −0.883363 −0.0892331
\(99\) 7.19747 0.723373
\(100\) −1.21967 −0.121967
\(101\) −14.5424 −1.44702 −0.723509 0.690315i \(-0.757472\pi\)
−0.723509 + 0.690315i \(0.757472\pi\)
\(102\) 14.2614 1.41209
\(103\) 4.66526 0.459681 0.229841 0.973228i \(-0.426179\pi\)
0.229841 + 0.973228i \(0.426179\pi\)
\(104\) 7.01688 0.688062
\(105\) 2.03323 0.198423
\(106\) −6.03544 −0.586213
\(107\) −7.94332 −0.767910 −0.383955 0.923352i \(-0.625438\pi\)
−0.383955 + 0.923352i \(0.625438\pi\)
\(108\) 4.62735 0.445266
\(109\) −5.47547 −0.524455 −0.262227 0.965006i \(-0.584457\pi\)
−0.262227 + 0.965006i \(0.584457\pi\)
\(110\) 5.60648 0.534557
\(111\) 21.1115 2.00382
\(112\) 0.0730644 0.00690394
\(113\) 18.4478 1.73543 0.867713 0.497065i \(-0.165589\pi\)
0.867713 + 0.497065i \(0.165589\pi\)
\(114\) 0.961269 0.0900311
\(115\) 7.18811 0.670294
\(116\) −4.52923 −0.420528
\(117\) 2.79784 0.258660
\(118\) 13.0009 1.19683
\(119\) 7.94029 0.727885
\(120\) −5.78280 −0.527895
\(121\) 29.2812 2.66193
\(122\) −8.17762 −0.740367
\(123\) −7.25078 −0.653781
\(124\) −9.12774 −0.819695
\(125\) −1.00000 −0.0894427
\(126\) 1.00177 0.0892447
\(127\) −6.10162 −0.541431 −0.270716 0.962659i \(-0.587260\pi\)
−0.270716 + 0.962659i \(0.587260\pi\)
\(128\) 6.73001 0.594855
\(129\) 1.82354 0.160554
\(130\) 2.17938 0.191144
\(131\) −11.9131 −1.04085 −0.520427 0.853906i \(-0.674227\pi\)
−0.520427 + 0.853906i \(0.674227\pi\)
\(132\) −15.7391 −1.36992
\(133\) 0.535203 0.0464080
\(134\) 1.47729 0.127618
\(135\) 3.79393 0.326530
\(136\) −22.5833 −1.93650
\(137\) −7.13296 −0.609410 −0.304705 0.952447i \(-0.598558\pi\)
−0.304705 + 0.952447i \(0.598558\pi\)
\(138\) 12.9104 1.09901
\(139\) 7.50424 0.636501 0.318250 0.948007i \(-0.396905\pi\)
0.318250 + 0.948007i \(0.396905\pi\)
\(140\) −1.21967 −0.103081
\(141\) 11.8151 0.995011
\(142\) 3.92086 0.329032
\(143\) 15.6583 1.30941
\(144\) −0.0828581 −0.00690484
\(145\) −3.71349 −0.308388
\(146\) 3.54125 0.293076
\(147\) 2.03323 0.167698
\(148\) −12.6641 −1.04098
\(149\) 19.8264 1.62424 0.812120 0.583490i \(-0.198313\pi\)
0.812120 + 0.583490i \(0.198313\pi\)
\(150\) −1.79608 −0.146650
\(151\) −21.0775 −1.71526 −0.857630 0.514268i \(-0.828064\pi\)
−0.857630 + 0.514268i \(0.828064\pi\)
\(152\) −1.52219 −0.123466
\(153\) −9.00462 −0.727980
\(154\) 5.60648 0.451783
\(155\) −7.48378 −0.601111
\(156\) −6.11820 −0.489848
\(157\) 10.4756 0.836042 0.418021 0.908437i \(-0.362724\pi\)
0.418021 + 0.908437i \(0.362724\pi\)
\(158\) −3.59001 −0.285606
\(159\) 13.8917 1.10169
\(160\) 5.62373 0.444595
\(161\) 7.18811 0.566502
\(162\) 9.81953 0.771495
\(163\) −0.101106 −0.00791920 −0.00395960 0.999992i \(-0.501260\pi\)
−0.00395960 + 0.999992i \(0.501260\pi\)
\(164\) 4.34950 0.339639
\(165\) −12.9044 −1.00461
\(166\) −13.0249 −1.01093
\(167\) 16.4514 1.27305 0.636524 0.771257i \(-0.280372\pi\)
0.636524 + 0.771257i \(0.280372\pi\)
\(168\) −5.78280 −0.446152
\(169\) −6.91322 −0.531786
\(170\) −7.01416 −0.537961
\(171\) −0.606942 −0.0464140
\(172\) −1.09388 −0.0834077
\(173\) −17.2459 −1.31118 −0.655591 0.755116i \(-0.727580\pi\)
−0.655591 + 0.755116i \(0.727580\pi\)
\(174\) −6.66973 −0.505631
\(175\) −1.00000 −0.0755929
\(176\) −0.463722 −0.0349543
\(177\) −29.9241 −2.24923
\(178\) 0.313864 0.0235251
\(179\) −17.8538 −1.33445 −0.667227 0.744855i \(-0.732519\pi\)
−0.667227 + 0.744855i \(0.732519\pi\)
\(180\) 1.38316 0.103094
\(181\) 3.50394 0.260446 0.130223 0.991485i \(-0.458431\pi\)
0.130223 + 0.991485i \(0.458431\pi\)
\(182\) 2.17938 0.161546
\(183\) 18.8224 1.39139
\(184\) −20.4440 −1.50715
\(185\) −10.3832 −0.763391
\(186\) −13.4415 −0.985578
\(187\) −50.3950 −3.68525
\(188\) −7.08749 −0.516908
\(189\) 3.79393 0.275968
\(190\) −0.472778 −0.0342989
\(191\) 0.526136 0.0380698 0.0190349 0.999819i \(-0.493941\pi\)
0.0190349 + 0.999819i \(0.493941\pi\)
\(192\) 10.3978 0.750397
\(193\) 27.1795 1.95642 0.978212 0.207609i \(-0.0665681\pi\)
0.978212 + 0.207609i \(0.0665681\pi\)
\(194\) −14.6273 −1.05018
\(195\) −5.01627 −0.359223
\(196\) −1.21967 −0.0871193
\(197\) −4.65848 −0.331903 −0.165951 0.986134i \(-0.553069\pi\)
−0.165951 + 0.986134i \(0.553069\pi\)
\(198\) −6.35798 −0.451842
\(199\) −2.75427 −0.195245 −0.0976226 0.995224i \(-0.531124\pi\)
−0.0976226 + 0.995224i \(0.531124\pi\)
\(200\) 2.84414 0.201111
\(201\) −3.40027 −0.239836
\(202\) 12.8462 0.903853
\(203\) −3.71349 −0.260636
\(204\) 19.6909 1.37864
\(205\) 3.56613 0.249069
\(206\) −4.12111 −0.287132
\(207\) −8.15161 −0.566576
\(208\) −0.180260 −0.0124988
\(209\) −3.39680 −0.234961
\(210\) −1.79608 −0.123942
\(211\) −17.3275 −1.19287 −0.596437 0.802660i \(-0.703417\pi\)
−0.596437 + 0.802660i \(0.703417\pi\)
\(212\) −8.33320 −0.572327
\(213\) −9.02464 −0.618358
\(214\) 7.01684 0.479661
\(215\) −0.896867 −0.0611658
\(216\) −10.7905 −0.734198
\(217\) −7.48378 −0.508032
\(218\) 4.83682 0.327591
\(219\) −8.15089 −0.550786
\(220\) 7.74094 0.521894
\(221\) −19.5898 −1.31775
\(222\) −18.6492 −1.25165
\(223\) 2.48021 0.166087 0.0830437 0.996546i \(-0.473536\pi\)
0.0830437 + 0.996546i \(0.473536\pi\)
\(224\) 5.62373 0.375751
\(225\) 1.13404 0.0756027
\(226\) −16.2961 −1.08400
\(227\) 18.5424 1.23070 0.615351 0.788253i \(-0.289014\pi\)
0.615351 + 0.788253i \(0.289014\pi\)
\(228\) 1.32724 0.0878983
\(229\) 1.00000 0.0660819
\(230\) −6.34971 −0.418687
\(231\) −12.9044 −0.849049
\(232\) 10.5617 0.693407
\(233\) 19.7062 1.29100 0.645498 0.763762i \(-0.276650\pi\)
0.645498 + 0.763762i \(0.276650\pi\)
\(234\) −2.47151 −0.161567
\(235\) −5.81099 −0.379067
\(236\) 17.9505 1.16848
\(237\) 8.26312 0.536747
\(238\) −7.01416 −0.454660
\(239\) 20.1134 1.30102 0.650512 0.759496i \(-0.274554\pi\)
0.650512 + 0.759496i \(0.274554\pi\)
\(240\) 0.148557 0.00958932
\(241\) 15.2440 0.981950 0.490975 0.871174i \(-0.336641\pi\)
0.490975 + 0.871174i \(0.336641\pi\)
\(242\) −25.8659 −1.66273
\(243\) −11.2198 −0.719750
\(244\) −11.2909 −0.722829
\(245\) −1.00000 −0.0638877
\(246\) 6.40507 0.408372
\(247\) −1.32042 −0.0840163
\(248\) 21.2849 1.35159
\(249\) 29.9795 1.89987
\(250\) 0.883363 0.0558688
\(251\) 27.3681 1.72746 0.863730 0.503955i \(-0.168122\pi\)
0.863730 + 0.503955i \(0.168122\pi\)
\(252\) 1.38316 0.0871306
\(253\) −45.6211 −2.86817
\(254\) 5.38994 0.338195
\(255\) 16.1445 1.01101
\(256\) −16.1729 −1.01081
\(257\) −3.58806 −0.223817 −0.111909 0.993718i \(-0.535696\pi\)
−0.111909 + 0.993718i \(0.535696\pi\)
\(258\) −1.61085 −0.100287
\(259\) −10.3832 −0.645183
\(260\) 3.00910 0.186616
\(261\) 4.21125 0.260670
\(262\) 10.5236 0.650150
\(263\) −12.5866 −0.776123 −0.388061 0.921634i \(-0.626855\pi\)
−0.388061 + 0.921634i \(0.626855\pi\)
\(264\) 36.7019 2.25885
\(265\) −6.83234 −0.419707
\(266\) −0.472778 −0.0289879
\(267\) −0.722420 −0.0442114
\(268\) 2.03971 0.124595
\(269\) 16.0251 0.977068 0.488534 0.872545i \(-0.337532\pi\)
0.488534 + 0.872545i \(0.337532\pi\)
\(270\) −3.35142 −0.203961
\(271\) 14.5842 0.885928 0.442964 0.896540i \(-0.353927\pi\)
0.442964 + 0.896540i \(0.353927\pi\)
\(272\) 0.580153 0.0351769
\(273\) −5.01627 −0.303599
\(274\) 6.30099 0.380657
\(275\) 6.34675 0.382723
\(276\) 17.8256 1.07298
\(277\) −11.8124 −0.709740 −0.354870 0.934916i \(-0.615475\pi\)
−0.354870 + 0.934916i \(0.615475\pi\)
\(278\) −6.62896 −0.397579
\(279\) 8.48691 0.508098
\(280\) 2.84414 0.169970
\(281\) −28.1359 −1.67845 −0.839223 0.543787i \(-0.816990\pi\)
−0.839223 + 0.543787i \(0.816990\pi\)
\(282\) −10.4370 −0.621515
\(283\) −3.46777 −0.206138 −0.103069 0.994674i \(-0.532866\pi\)
−0.103069 + 0.994674i \(0.532866\pi\)
\(284\) 5.41359 0.321237
\(285\) 1.08819 0.0644590
\(286\) −13.8320 −0.817902
\(287\) 3.56613 0.210502
\(288\) −6.37754 −0.375800
\(289\) 46.0483 2.70872
\(290\) 3.28036 0.192629
\(291\) 33.6677 1.97364
\(292\) 4.88945 0.286134
\(293\) 27.8880 1.62923 0.814617 0.580000i \(-0.196947\pi\)
0.814617 + 0.580000i \(0.196947\pi\)
\(294\) −1.79608 −0.104750
\(295\) 14.7175 0.856885
\(296\) 29.5313 1.71647
\(297\) −24.0791 −1.39721
\(298\) −17.5139 −1.01455
\(299\) −17.7341 −1.02559
\(300\) −2.47987 −0.143176
\(301\) −0.896867 −0.0516946
\(302\) 18.6190 1.07141
\(303\) −29.5680 −1.69864
\(304\) 0.0391043 0.00224278
\(305\) −9.25738 −0.530076
\(306\) 7.95434 0.454720
\(307\) 11.7107 0.668363 0.334181 0.942509i \(-0.391540\pi\)
0.334181 + 0.942509i \(0.391540\pi\)
\(308\) 7.74094 0.441081
\(309\) 9.48556 0.539615
\(310\) 6.61089 0.375473
\(311\) 1.46265 0.0829392 0.0414696 0.999140i \(-0.486796\pi\)
0.0414696 + 0.999140i \(0.486796\pi\)
\(312\) 14.2670 0.807708
\(313\) 16.5687 0.936518 0.468259 0.883591i \(-0.344881\pi\)
0.468259 + 0.883591i \(0.344881\pi\)
\(314\) −9.25374 −0.522219
\(315\) 1.13404 0.0638960
\(316\) −4.95677 −0.278840
\(317\) −12.1196 −0.680703 −0.340352 0.940298i \(-0.610546\pi\)
−0.340352 + 0.940298i \(0.610546\pi\)
\(318\) −12.2715 −0.688149
\(319\) 23.5686 1.31959
\(320\) −5.11392 −0.285877
\(321\) −16.1506 −0.901440
\(322\) −6.34971 −0.353855
\(323\) 4.24967 0.236458
\(324\) 13.5579 0.753219
\(325\) 2.46714 0.136852
\(326\) 0.0893129 0.00494659
\(327\) −11.1329 −0.615651
\(328\) −10.1426 −0.560029
\(329\) −5.81099 −0.320370
\(330\) 11.3993 0.627510
\(331\) 16.3250 0.897302 0.448651 0.893707i \(-0.351905\pi\)
0.448651 + 0.893707i \(0.351905\pi\)
\(332\) −17.9837 −0.986984
\(333\) 11.7750 0.645267
\(334\) −14.5326 −0.795186
\(335\) 1.67234 0.0913699
\(336\) 0.148557 0.00810445
\(337\) 18.4882 1.00712 0.503558 0.863961i \(-0.332024\pi\)
0.503558 + 0.863961i \(0.332024\pi\)
\(338\) 6.10688 0.332171
\(339\) 37.5088 2.03720
\(340\) −9.68454 −0.525218
\(341\) 47.4976 2.57214
\(342\) 0.536150 0.0289917
\(343\) −1.00000 −0.0539949
\(344\) 2.55081 0.137531
\(345\) 14.6151 0.786851
\(346\) 15.2344 0.819006
\(347\) 16.1260 0.865687 0.432843 0.901469i \(-0.357510\pi\)
0.432843 + 0.901469i \(0.357510\pi\)
\(348\) −9.20898 −0.493653
\(349\) 18.4447 0.987321 0.493661 0.869655i \(-0.335659\pi\)
0.493661 + 0.869655i \(0.335659\pi\)
\(350\) 0.883363 0.0472177
\(351\) −9.36016 −0.499608
\(352\) −35.6924 −1.90241
\(353\) 5.94436 0.316386 0.158193 0.987408i \(-0.449433\pi\)
0.158193 + 0.987408i \(0.449433\pi\)
\(354\) 26.4338 1.40494
\(355\) 4.43857 0.235575
\(356\) 0.433356 0.0229678
\(357\) 16.1445 0.854456
\(358\) 15.7714 0.833542
\(359\) −25.5133 −1.34654 −0.673269 0.739398i \(-0.735110\pi\)
−0.673269 + 0.739398i \(0.735110\pi\)
\(360\) −3.22537 −0.169992
\(361\) −18.7136 −0.984924
\(362\) −3.09525 −0.162683
\(363\) 59.5356 3.12481
\(364\) 3.00910 0.157720
\(365\) 4.00883 0.209832
\(366\) −16.6270 −0.869108
\(367\) 21.1556 1.10431 0.552157 0.833740i \(-0.313805\pi\)
0.552157 + 0.833740i \(0.313805\pi\)
\(368\) 0.525195 0.0273777
\(369\) −4.04414 −0.210529
\(370\) 9.17216 0.476838
\(371\) −6.83234 −0.354717
\(372\) −18.5588 −0.962231
\(373\) 5.42023 0.280649 0.140324 0.990106i \(-0.455185\pi\)
0.140324 + 0.990106i \(0.455185\pi\)
\(374\) 44.5171 2.30192
\(375\) −2.03323 −0.104996
\(376\) 16.5272 0.852327
\(377\) 9.16169 0.471851
\(378\) −3.35142 −0.172378
\(379\) −24.1972 −1.24293 −0.621464 0.783443i \(-0.713462\pi\)
−0.621464 + 0.783443i \(0.713462\pi\)
\(380\) −0.652771 −0.0334864
\(381\) −12.4060 −0.635580
\(382\) −0.464769 −0.0237796
\(383\) 21.8000 1.11393 0.556964 0.830537i \(-0.311966\pi\)
0.556964 + 0.830537i \(0.311966\pi\)
\(384\) 13.6837 0.698293
\(385\) 6.34675 0.323460
\(386\) −24.0094 −1.22204
\(387\) 1.01708 0.0517013
\(388\) −20.1962 −1.02530
\(389\) 5.75464 0.291772 0.145886 0.989301i \(-0.453397\pi\)
0.145886 + 0.989301i \(0.453397\pi\)
\(390\) 4.43119 0.224382
\(391\) 57.0757 2.88644
\(392\) 2.84414 0.143651
\(393\) −24.2221 −1.22185
\(394\) 4.11512 0.207317
\(395\) −4.06403 −0.204483
\(396\) −8.77854 −0.441138
\(397\) 15.9853 0.802281 0.401141 0.916016i \(-0.368614\pi\)
0.401141 + 0.916016i \(0.368614\pi\)
\(398\) 2.43302 0.121956
\(399\) 1.08819 0.0544778
\(400\) −0.0730644 −0.00365322
\(401\) −8.19554 −0.409266 −0.204633 0.978839i \(-0.565600\pi\)
−0.204633 + 0.978839i \(0.565600\pi\)
\(402\) 3.00367 0.149809
\(403\) 18.4635 0.919734
\(404\) 17.7369 0.882442
\(405\) 11.1161 0.552362
\(406\) 3.28036 0.162801
\(407\) 65.8998 3.26653
\(408\) −45.9171 −2.27323
\(409\) 3.00358 0.148517 0.0742587 0.997239i \(-0.476341\pi\)
0.0742587 + 0.997239i \(0.476341\pi\)
\(410\) −3.15019 −0.155577
\(411\) −14.5030 −0.715379
\(412\) −5.69008 −0.280330
\(413\) 14.7175 0.724200
\(414\) 7.20083 0.353901
\(415\) −14.7447 −0.723790
\(416\) −13.8745 −0.680255
\(417\) 15.2579 0.747181
\(418\) 3.00060 0.146764
\(419\) −0.841884 −0.0411287 −0.0205644 0.999789i \(-0.506546\pi\)
−0.0205644 + 0.999789i \(0.506546\pi\)
\(420\) −2.47987 −0.121006
\(421\) 17.7951 0.867282 0.433641 0.901086i \(-0.357229\pi\)
0.433641 + 0.901086i \(0.357229\pi\)
\(422\) 15.3065 0.745107
\(423\) 6.58990 0.320412
\(424\) 19.4321 0.943707
\(425\) −7.94029 −0.385161
\(426\) 7.97203 0.386246
\(427\) −9.25738 −0.447996
\(428\) 9.68823 0.468298
\(429\) 31.8370 1.53711
\(430\) 0.792259 0.0382061
\(431\) −6.80837 −0.327948 −0.163974 0.986465i \(-0.552431\pi\)
−0.163974 + 0.986465i \(0.552431\pi\)
\(432\) 0.277201 0.0133369
\(433\) 41.0604 1.97324 0.986620 0.163039i \(-0.0521296\pi\)
0.986620 + 0.163039i \(0.0521296\pi\)
\(434\) 6.61089 0.317333
\(435\) −7.55039 −0.362013
\(436\) 6.67826 0.319831
\(437\) 3.84709 0.184031
\(438\) 7.20020 0.344039
\(439\) −35.2380 −1.68182 −0.840909 0.541177i \(-0.817979\pi\)
−0.840909 + 0.541177i \(0.817979\pi\)
\(440\) −18.0510 −0.860549
\(441\) 1.13404 0.0540020
\(442\) 17.3049 0.823111
\(443\) 10.2041 0.484810 0.242405 0.970175i \(-0.422064\pi\)
0.242405 + 0.970175i \(0.422064\pi\)
\(444\) −25.7491 −1.22200
\(445\) 0.355306 0.0168431
\(446\) −2.19093 −0.103743
\(447\) 40.3117 1.90668
\(448\) −5.11392 −0.241610
\(449\) 15.9792 0.754105 0.377053 0.926192i \(-0.376938\pi\)
0.377053 + 0.926192i \(0.376938\pi\)
\(450\) −1.00177 −0.0472239
\(451\) −22.6333 −1.06576
\(452\) −22.5003 −1.05832
\(453\) −42.8554 −2.01352
\(454\) −16.3797 −0.768736
\(455\) 2.46714 0.115661
\(456\) −3.09497 −0.144935
\(457\) −10.3973 −0.486366 −0.243183 0.969980i \(-0.578192\pi\)
−0.243183 + 0.969980i \(0.578192\pi\)
\(458\) −0.883363 −0.0412768
\(459\) 30.1249 1.40611
\(460\) −8.76712 −0.408769
\(461\) 8.46250 0.394138 0.197069 0.980390i \(-0.436858\pi\)
0.197069 + 0.980390i \(0.436858\pi\)
\(462\) 11.3993 0.530343
\(463\) −35.0123 −1.62716 −0.813579 0.581454i \(-0.802484\pi\)
−0.813579 + 0.581454i \(0.802484\pi\)
\(464\) −0.271324 −0.0125959
\(465\) −15.2163 −0.705638
\(466\) −17.4077 −0.806398
\(467\) 30.9980 1.43441 0.717207 0.696860i \(-0.245420\pi\)
0.717207 + 0.696860i \(0.245420\pi\)
\(468\) −3.41244 −0.157740
\(469\) 1.67234 0.0772217
\(470\) 5.13321 0.236777
\(471\) 21.2993 0.981420
\(472\) −41.8585 −1.92670
\(473\) 5.69219 0.261727
\(474\) −7.29933 −0.335270
\(475\) −0.535203 −0.0245568
\(476\) −9.68454 −0.443890
\(477\) 7.74815 0.354764
\(478\) −17.7674 −0.812661
\(479\) −32.1527 −1.46910 −0.734548 0.678557i \(-0.762606\pi\)
−0.734548 + 0.678557i \(0.762606\pi\)
\(480\) 11.4344 0.521905
\(481\) 25.6169 1.16803
\(482\) −13.4660 −0.613357
\(483\) 14.6151 0.665010
\(484\) −35.7134 −1.62334
\(485\) −16.5587 −0.751892
\(486\) 9.91114 0.449579
\(487\) −12.0181 −0.544593 −0.272296 0.962213i \(-0.587783\pi\)
−0.272296 + 0.962213i \(0.587783\pi\)
\(488\) 26.3292 1.19187
\(489\) −0.205571 −0.00929626
\(490\) 0.883363 0.0399063
\(491\) 7.13139 0.321835 0.160917 0.986968i \(-0.448555\pi\)
0.160917 + 0.986968i \(0.448555\pi\)
\(492\) 8.84356 0.398698
\(493\) −29.4862 −1.32799
\(494\) 1.16641 0.0524793
\(495\) −7.19747 −0.323502
\(496\) −0.546798 −0.0245520
\(497\) 4.43857 0.199097
\(498\) −26.4827 −1.18672
\(499\) −3.66662 −0.164140 −0.0820702 0.996627i \(-0.526153\pi\)
−0.0820702 + 0.996627i \(0.526153\pi\)
\(500\) 1.21967 0.0545453
\(501\) 33.4495 1.49442
\(502\) −24.1760 −1.07903
\(503\) 17.7006 0.789229 0.394615 0.918847i \(-0.370878\pi\)
0.394615 + 0.918847i \(0.370878\pi\)
\(504\) −3.22537 −0.143669
\(505\) 14.5424 0.647126
\(506\) 40.3000 1.79155
\(507\) −14.0562 −0.624257
\(508\) 7.44196 0.330184
\(509\) 17.4283 0.772495 0.386247 0.922395i \(-0.373771\pi\)
0.386247 + 0.922395i \(0.373771\pi\)
\(510\) −14.2614 −0.631507
\(511\) 4.00883 0.177340
\(512\) 0.826505 0.0365267
\(513\) 2.03052 0.0896497
\(514\) 3.16956 0.139803
\(515\) −4.66526 −0.205576
\(516\) −2.22412 −0.0979113
\(517\) 36.8809 1.62202
\(518\) 9.17216 0.403002
\(519\) −35.0649 −1.53918
\(520\) −7.01688 −0.307711
\(521\) 31.8144 1.39382 0.696908 0.717161i \(-0.254559\pi\)
0.696908 + 0.717161i \(0.254559\pi\)
\(522\) −3.72006 −0.162823
\(523\) 28.7279 1.25618 0.628092 0.778139i \(-0.283836\pi\)
0.628092 + 0.778139i \(0.283836\pi\)
\(524\) 14.5301 0.634749
\(525\) −2.03323 −0.0887376
\(526\) 11.1185 0.484791
\(527\) −59.4234 −2.58852
\(528\) −0.942855 −0.0410325
\(529\) 28.6689 1.24647
\(530\) 6.03544 0.262163
\(531\) −16.6902 −0.724294
\(532\) −0.652771 −0.0283012
\(533\) −8.79814 −0.381090
\(534\) 0.638159 0.0276158
\(535\) 7.94332 0.343420
\(536\) −4.75637 −0.205444
\(537\) −36.3009 −1.56650
\(538\) −14.1560 −0.610308
\(539\) 6.34675 0.273374
\(540\) −4.62735 −0.199129
\(541\) −16.3684 −0.703732 −0.351866 0.936050i \(-0.614453\pi\)
−0.351866 + 0.936050i \(0.614453\pi\)
\(542\) −12.8831 −0.553379
\(543\) 7.12432 0.305734
\(544\) 44.6541 1.91453
\(545\) 5.47547 0.234543
\(546\) 4.43119 0.189637
\(547\) 1.47261 0.0629642 0.0314821 0.999504i \(-0.489977\pi\)
0.0314821 + 0.999504i \(0.489977\pi\)
\(548\) 8.69986 0.371640
\(549\) 10.4982 0.448054
\(550\) −5.60648 −0.239061
\(551\) −1.98747 −0.0846690
\(552\) −41.5673 −1.76922
\(553\) −4.06403 −0.172820
\(554\) 10.4347 0.443326
\(555\) −21.1115 −0.896135
\(556\) −9.15269 −0.388161
\(557\) −38.1285 −1.61556 −0.807778 0.589486i \(-0.799330\pi\)
−0.807778 + 0.589486i \(0.799330\pi\)
\(558\) −7.49702 −0.317374
\(559\) 2.21270 0.0935871
\(560\) −0.0730644 −0.00308754
\(561\) −102.465 −4.32607
\(562\) 24.8542 1.04841
\(563\) 34.7247 1.46347 0.731735 0.681589i \(-0.238711\pi\)
0.731735 + 0.681589i \(0.238711\pi\)
\(564\) −14.4105 −0.606792
\(565\) −18.4478 −0.776106
\(566\) 3.06330 0.128760
\(567\) 11.1161 0.466831
\(568\) −12.6239 −0.529687
\(569\) 2.03097 0.0851426 0.0425713 0.999093i \(-0.486445\pi\)
0.0425713 + 0.999093i \(0.486445\pi\)
\(570\) −0.961269 −0.0402631
\(571\) 24.6002 1.02949 0.514743 0.857344i \(-0.327887\pi\)
0.514743 + 0.857344i \(0.327887\pi\)
\(572\) −19.0980 −0.798527
\(573\) 1.06976 0.0446897
\(574\) −3.15019 −0.131486
\(575\) −7.18811 −0.299765
\(576\) 5.79940 0.241642
\(577\) −46.4646 −1.93435 −0.967173 0.254117i \(-0.918215\pi\)
−0.967173 + 0.254117i \(0.918215\pi\)
\(578\) −40.6773 −1.69195
\(579\) 55.2623 2.29662
\(580\) 4.52923 0.188066
\(581\) −14.7447 −0.611714
\(582\) −29.7408 −1.23280
\(583\) 43.3631 1.79592
\(584\) −11.4017 −0.471804
\(585\) −2.79784 −0.115676
\(586\) −24.6352 −1.01767
\(587\) 26.7098 1.10243 0.551215 0.834363i \(-0.314164\pi\)
0.551215 + 0.834363i \(0.314164\pi\)
\(588\) −2.47987 −0.102268
\(589\) −4.00534 −0.165037
\(590\) −13.0009 −0.535238
\(591\) −9.47177 −0.389617
\(592\) −0.758645 −0.0311801
\(593\) −11.9743 −0.491727 −0.245863 0.969305i \(-0.579071\pi\)
−0.245863 + 0.969305i \(0.579071\pi\)
\(594\) 21.2706 0.872744
\(595\) −7.94029 −0.325520
\(596\) −24.1816 −0.990519
\(597\) −5.60008 −0.229196
\(598\) 15.6656 0.640615
\(599\) −11.5055 −0.470103 −0.235051 0.971983i \(-0.575526\pi\)
−0.235051 + 0.971983i \(0.575526\pi\)
\(600\) 5.78280 0.236082
\(601\) 18.3865 0.749999 0.375000 0.927025i \(-0.377643\pi\)
0.375000 + 0.927025i \(0.377643\pi\)
\(602\) 0.792259 0.0322901
\(603\) −1.89651 −0.0772317
\(604\) 25.7075 1.04603
\(605\) −29.2812 −1.19045
\(606\) 26.1193 1.06102
\(607\) 26.4097 1.07193 0.535967 0.844239i \(-0.319947\pi\)
0.535967 + 0.844239i \(0.319947\pi\)
\(608\) 3.00984 0.122065
\(609\) −7.55039 −0.305957
\(610\) 8.17762 0.331102
\(611\) 14.3365 0.579993
\(612\) 10.9827 0.443948
\(613\) −7.19441 −0.290579 −0.145290 0.989389i \(-0.546411\pi\)
−0.145290 + 0.989389i \(0.546411\pi\)
\(614\) −10.3448 −0.417481
\(615\) 7.25078 0.292380
\(616\) −18.0510 −0.727296
\(617\) 0.00674299 0.000271462 0 0.000135731 1.00000i \(-0.499957\pi\)
0.000135731 1.00000i \(0.499957\pi\)
\(618\) −8.37919 −0.337061
\(619\) 26.2491 1.05504 0.527520 0.849543i \(-0.323122\pi\)
0.527520 + 0.849543i \(0.323122\pi\)
\(620\) 9.12774 0.366579
\(621\) 27.2712 1.09435
\(622\) −1.29205 −0.0518065
\(623\) 0.355306 0.0142350
\(624\) −0.366511 −0.0146722
\(625\) 1.00000 0.0400000
\(626\) −14.6362 −0.584979
\(627\) −6.90648 −0.275818
\(628\) −12.7768 −0.509848
\(629\) −82.4459 −3.28733
\(630\) −1.00177 −0.0399115
\(631\) −3.62995 −0.144506 −0.0722529 0.997386i \(-0.523019\pi\)
−0.0722529 + 0.997386i \(0.523019\pi\)
\(632\) 11.5587 0.459779
\(633\) −35.2309 −1.40030
\(634\) 10.7060 0.425189
\(635\) 6.10162 0.242135
\(636\) −16.9434 −0.671848
\(637\) 2.46714 0.0977517
\(638\) −20.8196 −0.824255
\(639\) −5.03352 −0.199123
\(640\) −6.73001 −0.266027
\(641\) −1.40605 −0.0555356 −0.0277678 0.999614i \(-0.508840\pi\)
−0.0277678 + 0.999614i \(0.508840\pi\)
\(642\) 14.2669 0.563068
\(643\) −13.4476 −0.530320 −0.265160 0.964204i \(-0.585425\pi\)
−0.265160 + 0.964204i \(0.585425\pi\)
\(644\) −8.76712 −0.345473
\(645\) −1.82354 −0.0718018
\(646\) −3.75400 −0.147699
\(647\) 24.7870 0.974478 0.487239 0.873269i \(-0.338004\pi\)
0.487239 + 0.873269i \(0.338004\pi\)
\(648\) −31.6156 −1.24198
\(649\) −93.4082 −3.66659
\(650\) −2.17938 −0.0854823
\(651\) −15.2163 −0.596373
\(652\) 0.123316 0.00482941
\(653\) 32.4803 1.27105 0.635526 0.772079i \(-0.280783\pi\)
0.635526 + 0.772079i \(0.280783\pi\)
\(654\) 9.83440 0.384555
\(655\) 11.9131 0.465484
\(656\) 0.260557 0.0101731
\(657\) −4.54618 −0.177363
\(658\) 5.13321 0.200113
\(659\) 25.4356 0.990832 0.495416 0.868656i \(-0.335016\pi\)
0.495416 + 0.868656i \(0.335016\pi\)
\(660\) 15.7391 0.612645
\(661\) 19.1624 0.745330 0.372665 0.927966i \(-0.378444\pi\)
0.372665 + 0.927966i \(0.378444\pi\)
\(662\) −14.4209 −0.560483
\(663\) −39.8307 −1.54690
\(664\) 41.9360 1.62743
\(665\) −0.535203 −0.0207543
\(666\) −10.4016 −0.403054
\(667\) −26.6929 −1.03355
\(668\) −20.0653 −0.776349
\(669\) 5.04285 0.194968
\(670\) −1.47729 −0.0570725
\(671\) 58.7542 2.26818
\(672\) 11.4344 0.441090
\(673\) 9.58214 0.369364 0.184682 0.982798i \(-0.440874\pi\)
0.184682 + 0.982798i \(0.440874\pi\)
\(674\) −16.3318 −0.629077
\(675\) −3.79393 −0.146028
\(676\) 8.43185 0.324302
\(677\) −13.1672 −0.506058 −0.253029 0.967459i \(-0.581427\pi\)
−0.253029 + 0.967459i \(0.581427\pi\)
\(678\) −33.1338 −1.27250
\(679\) −16.5587 −0.635465
\(680\) 22.5833 0.866029
\(681\) 37.7010 1.44471
\(682\) −41.9577 −1.60664
\(683\) 26.9407 1.03086 0.515429 0.856932i \(-0.327633\pi\)
0.515429 + 0.856932i \(0.327633\pi\)
\(684\) 0.740269 0.0283049
\(685\) 7.13296 0.272536
\(686\) 0.883363 0.0337269
\(687\) 2.03323 0.0775727
\(688\) −0.0655291 −0.00249827
\(689\) 16.8563 0.642176
\(690\) −12.9104 −0.491492
\(691\) −8.22149 −0.312760 −0.156380 0.987697i \(-0.549983\pi\)
−0.156380 + 0.987697i \(0.549983\pi\)
\(692\) 21.0343 0.799604
\(693\) −7.19747 −0.273409
\(694\) −14.2451 −0.540735
\(695\) −7.50424 −0.284652
\(696\) 21.4743 0.813983
\(697\) 28.3161 1.07255
\(698\) −16.2933 −0.616712
\(699\) 40.0673 1.51549
\(700\) 1.21967 0.0460992
\(701\) 3.90696 0.147564 0.0737820 0.997274i \(-0.476493\pi\)
0.0737820 + 0.997274i \(0.476493\pi\)
\(702\) 8.26842 0.312071
\(703\) −5.55713 −0.209591
\(704\) 32.4568 1.22326
\(705\) −11.8151 −0.444982
\(706\) −5.25102 −0.197625
\(707\) 14.5424 0.546921
\(708\) 36.4975 1.37166
\(709\) −20.9681 −0.787473 −0.393736 0.919223i \(-0.628818\pi\)
−0.393736 + 0.919223i \(0.628818\pi\)
\(710\) −3.92086 −0.147147
\(711\) 4.60877 0.172843
\(712\) −1.01054 −0.0378715
\(713\) −53.7942 −2.01461
\(714\) −14.2614 −0.533721
\(715\) −15.6583 −0.585588
\(716\) 21.7757 0.813797
\(717\) 40.8952 1.52726
\(718\) 22.5375 0.841091
\(719\) 47.3428 1.76559 0.882794 0.469760i \(-0.155660\pi\)
0.882794 + 0.469760i \(0.155660\pi\)
\(720\) 0.0828581 0.00308794
\(721\) −4.66526 −0.173743
\(722\) 16.5309 0.615215
\(723\) 30.9946 1.15270
\(724\) −4.27365 −0.158829
\(725\) 3.71349 0.137915
\(726\) −52.5915 −1.95185
\(727\) −16.4317 −0.609418 −0.304709 0.952446i \(-0.598559\pi\)
−0.304709 + 0.952446i \(0.598559\pi\)
\(728\) −7.01688 −0.260063
\(729\) 10.5358 0.390214
\(730\) −3.54125 −0.131068
\(731\) −7.12139 −0.263394
\(732\) −22.9571 −0.848520
\(733\) 13.1146 0.484400 0.242200 0.970226i \(-0.422131\pi\)
0.242200 + 0.970226i \(0.422131\pi\)
\(734\) −18.6881 −0.689790
\(735\) −2.03323 −0.0749970
\(736\) 40.4240 1.49005
\(737\) −10.6139 −0.390970
\(738\) 3.57244 0.131503
\(739\) −19.6675 −0.723480 −0.361740 0.932279i \(-0.617817\pi\)
−0.361740 + 0.932279i \(0.617817\pi\)
\(740\) 12.6641 0.465542
\(741\) −2.68472 −0.0986258
\(742\) 6.03544 0.221568
\(743\) −20.4652 −0.750796 −0.375398 0.926864i \(-0.622494\pi\)
−0.375398 + 0.926864i \(0.622494\pi\)
\(744\) 43.2772 1.58662
\(745\) −19.8264 −0.726382
\(746\) −4.78803 −0.175302
\(747\) 16.7211 0.611794
\(748\) 61.4653 2.24739
\(749\) 7.94332 0.290243
\(750\) 1.79608 0.0655837
\(751\) 0.387677 0.0141465 0.00707327 0.999975i \(-0.497748\pi\)
0.00707327 + 0.999975i \(0.497748\pi\)
\(752\) −0.424576 −0.0154827
\(753\) 55.6458 2.02784
\(754\) −8.09310 −0.294733
\(755\) 21.0775 0.767087
\(756\) −4.62735 −0.168295
\(757\) 8.89702 0.323368 0.161684 0.986843i \(-0.448308\pi\)
0.161684 + 0.986843i \(0.448308\pi\)
\(758\) 21.3749 0.776372
\(759\) −92.7584 −3.36692
\(760\) 1.52219 0.0552156
\(761\) −16.8698 −0.611528 −0.305764 0.952107i \(-0.598912\pi\)
−0.305764 + 0.952107i \(0.598912\pi\)
\(762\) 10.9590 0.397003
\(763\) 5.47547 0.198225
\(764\) −0.641712 −0.0232163
\(765\) 9.00462 0.325563
\(766\) −19.2573 −0.695794
\(767\) −36.3101 −1.31108
\(768\) −32.8833 −1.18657
\(769\) −54.5340 −1.96655 −0.983273 0.182139i \(-0.941698\pi\)
−0.983273 + 0.182139i \(0.941698\pi\)
\(770\) −5.60648 −0.202044
\(771\) −7.29538 −0.262737
\(772\) −33.1500 −1.19310
\(773\) 48.8413 1.75670 0.878349 0.478019i \(-0.158645\pi\)
0.878349 + 0.478019i \(0.158645\pi\)
\(774\) −0.898454 −0.0322943
\(775\) 7.48378 0.268825
\(776\) 47.0952 1.69062
\(777\) −21.1115 −0.757373
\(778\) −5.08343 −0.182250
\(779\) 1.90860 0.0683828
\(780\) 6.11820 0.219067
\(781\) −28.1705 −1.00802
\(782\) −50.4185 −1.80296
\(783\) −14.0887 −0.503490
\(784\) −0.0730644 −0.00260944
\(785\) −10.4756 −0.373889
\(786\) 21.3969 0.763204
\(787\) 13.5692 0.483691 0.241846 0.970315i \(-0.422247\pi\)
0.241846 + 0.970315i \(0.422247\pi\)
\(788\) 5.68180 0.202406
\(789\) −25.5915 −0.911081
\(790\) 3.59001 0.127727
\(791\) −18.4478 −0.655929
\(792\) 20.4706 0.727391
\(793\) 22.8392 0.811045
\(794\) −14.1209 −0.501131
\(795\) −13.8917 −0.492690
\(796\) 3.35931 0.119067
\(797\) −4.81564 −0.170579 −0.0852894 0.996356i \(-0.527181\pi\)
−0.0852894 + 0.996356i \(0.527181\pi\)
\(798\) −0.961269 −0.0340285
\(799\) −46.1409 −1.63235
\(800\) −5.62373 −0.198829
\(801\) −0.402931 −0.0142369
\(802\) 7.23964 0.255640
\(803\) −25.4430 −0.897865
\(804\) 4.14720 0.146261
\(805\) −7.18811 −0.253347
\(806\) −16.3100 −0.574495
\(807\) 32.5828 1.14697
\(808\) −41.3604 −1.45505
\(809\) −36.0292 −1.26672 −0.633359 0.773858i \(-0.718324\pi\)
−0.633359 + 0.773858i \(0.718324\pi\)
\(810\) −9.81953 −0.345023
\(811\) 11.5956 0.407176 0.203588 0.979057i \(-0.434740\pi\)
0.203588 + 0.979057i \(0.434740\pi\)
\(812\) 4.52923 0.158945
\(813\) 29.6531 1.03998
\(814\) −58.2134 −2.04038
\(815\) 0.101106 0.00354158
\(816\) 1.17959 0.0412938
\(817\) −0.480006 −0.0167933
\(818\) −2.65325 −0.0927687
\(819\) −2.79784 −0.0977644
\(820\) −4.34950 −0.151891
\(821\) −12.4009 −0.432793 −0.216396 0.976306i \(-0.569430\pi\)
−0.216396 + 0.976306i \(0.569430\pi\)
\(822\) 12.8114 0.446849
\(823\) 1.63432 0.0569689 0.0284845 0.999594i \(-0.490932\pi\)
0.0284845 + 0.999594i \(0.490932\pi\)
\(824\) 13.2686 0.462235
\(825\) 12.9044 0.449274
\(826\) −13.0009 −0.452358
\(827\) 36.2608 1.26091 0.630456 0.776225i \(-0.282868\pi\)
0.630456 + 0.776225i \(0.282868\pi\)
\(828\) 9.94227 0.345518
\(829\) −36.5218 −1.26845 −0.634227 0.773147i \(-0.718681\pi\)
−0.634227 + 0.773147i \(0.718681\pi\)
\(830\) 13.0249 0.452102
\(831\) −24.0174 −0.833155
\(832\) 12.6168 0.437408
\(833\) −7.94029 −0.275115
\(834\) −13.4782 −0.466713
\(835\) −16.4514 −0.569324
\(836\) 4.14297 0.143288
\(837\) −28.3929 −0.981403
\(838\) 0.743689 0.0256903
\(839\) 7.44914 0.257173 0.128586 0.991698i \(-0.458956\pi\)
0.128586 + 0.991698i \(0.458956\pi\)
\(840\) 5.78280 0.199525
\(841\) −15.2100 −0.524483
\(842\) −15.7196 −0.541732
\(843\) −57.2069 −1.97031
\(844\) 21.1338 0.727456
\(845\) 6.91322 0.237822
\(846\) −5.82127 −0.200139
\(847\) −29.2812 −1.00611
\(848\) −0.499201 −0.0171426
\(849\) −7.05079 −0.241983
\(850\) 7.01416 0.240584
\(851\) −74.6358 −2.55848
\(852\) 11.0071 0.377097
\(853\) 10.7573 0.368322 0.184161 0.982896i \(-0.441043\pi\)
0.184161 + 0.982896i \(0.441043\pi\)
\(854\) 8.17762 0.279832
\(855\) 0.606942 0.0207570
\(856\) −22.5919 −0.772175
\(857\) −50.2212 −1.71552 −0.857762 0.514046i \(-0.828146\pi\)
−0.857762 + 0.514046i \(0.828146\pi\)
\(858\) −28.1236 −0.960125
\(859\) −7.06714 −0.241128 −0.120564 0.992706i \(-0.538470\pi\)
−0.120564 + 0.992706i \(0.538470\pi\)
\(860\) 1.09388 0.0373011
\(861\) 7.25078 0.247106
\(862\) 6.01426 0.204847
\(863\) −45.8402 −1.56042 −0.780210 0.625518i \(-0.784888\pi\)
−0.780210 + 0.625518i \(0.784888\pi\)
\(864\) 21.3361 0.725867
\(865\) 17.2459 0.586378
\(866\) −36.2713 −1.23255
\(867\) 93.6269 3.17974
\(868\) 9.12774 0.309816
\(869\) 25.7934 0.874980
\(870\) 6.66973 0.226125
\(871\) −4.12591 −0.139801
\(872\) −15.5730 −0.527368
\(873\) 18.7782 0.635547
\(874\) −3.39838 −0.114952
\(875\) 1.00000 0.0338062
\(876\) 9.94140 0.335889
\(877\) −23.7509 −0.802010 −0.401005 0.916076i \(-0.631339\pi\)
−0.401005 + 0.916076i \(0.631339\pi\)
\(878\) 31.1279 1.05052
\(879\) 56.7028 1.91254
\(880\) 0.463722 0.0156321
\(881\) −6.36334 −0.214386 −0.107193 0.994238i \(-0.534186\pi\)
−0.107193 + 0.994238i \(0.534186\pi\)
\(882\) −1.00177 −0.0337313
\(883\) 33.0357 1.11174 0.555870 0.831269i \(-0.312385\pi\)
0.555870 + 0.831269i \(0.312385\pi\)
\(884\) 23.8931 0.803612
\(885\) 29.9241 1.00589
\(886\) −9.01390 −0.302828
\(887\) 0.411785 0.0138264 0.00691319 0.999976i \(-0.497799\pi\)
0.00691319 + 0.999976i \(0.497799\pi\)
\(888\) 60.0441 2.01495
\(889\) 6.10162 0.204642
\(890\) −0.313864 −0.0105207
\(891\) −70.5509 −2.36354
\(892\) −3.02504 −0.101286
\(893\) −3.11006 −0.104074
\(894\) −35.6098 −1.19097
\(895\) 17.8538 0.596786
\(896\) −6.73001 −0.224834
\(897\) −36.0575 −1.20393
\(898\) −14.1154 −0.471038
\(899\) 27.7909 0.926879
\(900\) −1.38316 −0.0461052
\(901\) −54.2508 −1.80736
\(902\) 19.9934 0.665709
\(903\) −1.82354 −0.0606836
\(904\) 52.4682 1.74507
\(905\) −3.50394 −0.116475
\(906\) 37.8569 1.25771
\(907\) 33.2480 1.10398 0.551990 0.833851i \(-0.313869\pi\)
0.551990 + 0.833851i \(0.313869\pi\)
\(908\) −22.6156 −0.750525
\(909\) −16.4916 −0.546993
\(910\) −2.17938 −0.0722457
\(911\) −14.7819 −0.489745 −0.244873 0.969555i \(-0.578746\pi\)
−0.244873 + 0.969555i \(0.578746\pi\)
\(912\) 0.0795082 0.00263278
\(913\) 93.5810 3.09708
\(914\) 9.18460 0.303800
\(915\) −18.8224 −0.622250
\(916\) −1.21967 −0.0402990
\(917\) 11.9131 0.393406
\(918\) −26.6112 −0.878302
\(919\) 40.9568 1.35104 0.675520 0.737342i \(-0.263919\pi\)
0.675520 + 0.737342i \(0.263919\pi\)
\(920\) 20.4440 0.674017
\(921\) 23.8105 0.784583
\(922\) −7.47546 −0.246191
\(923\) −10.9506 −0.360442
\(924\) 15.7391 0.517780
\(925\) 10.3832 0.341399
\(926\) 30.9286 1.01638
\(927\) 5.29059 0.173766
\(928\) −20.8836 −0.685539
\(929\) −22.7330 −0.745845 −0.372922 0.927863i \(-0.621644\pi\)
−0.372922 + 0.927863i \(0.621644\pi\)
\(930\) 13.4415 0.440764
\(931\) −0.535203 −0.0175406
\(932\) −24.0351 −0.787295
\(933\) 2.97391 0.0973614
\(934\) −27.3824 −0.895981
\(935\) 50.3950 1.64809
\(936\) 7.95743 0.260097
\(937\) −32.4556 −1.06028 −0.530140 0.847910i \(-0.677861\pi\)
−0.530140 + 0.847910i \(0.677861\pi\)
\(938\) −1.47729 −0.0482351
\(939\) 33.6880 1.09937
\(940\) 7.08749 0.231168
\(941\) 6.41991 0.209283 0.104642 0.994510i \(-0.466630\pi\)
0.104642 + 0.994510i \(0.466630\pi\)
\(942\) −18.8150 −0.613026
\(943\) 25.6337 0.834749
\(944\) 1.07532 0.0349988
\(945\) −3.79393 −0.123417
\(946\) −5.02827 −0.163483
\(947\) 14.0363 0.456118 0.228059 0.973647i \(-0.426762\pi\)
0.228059 + 0.973647i \(0.426762\pi\)
\(948\) −10.0783 −0.327327
\(949\) −9.89035 −0.321054
\(950\) 0.472778 0.0153389
\(951\) −24.6419 −0.799070
\(952\) 22.5833 0.731928
\(953\) −56.8548 −1.84171 −0.920854 0.389908i \(-0.872507\pi\)
−0.920854 + 0.389908i \(0.872507\pi\)
\(954\) −6.84443 −0.221597
\(955\) −0.526136 −0.0170254
\(956\) −24.5317 −0.793410
\(957\) 47.9204 1.54905
\(958\) 28.4025 0.917644
\(959\) 7.13296 0.230335
\(960\) −10.3978 −0.335588
\(961\) 25.0069 0.806675
\(962\) −22.6290 −0.729589
\(963\) −9.00805 −0.290280
\(964\) −18.5926 −0.598828
\(965\) −27.1795 −0.874939
\(966\) −12.9104 −0.415387
\(967\) −27.3680 −0.880095 −0.440048 0.897974i \(-0.645038\pi\)
−0.440048 + 0.897974i \(0.645038\pi\)
\(968\) 83.2798 2.67671
\(969\) 8.64057 0.277575
\(970\) 14.6273 0.469656
\(971\) −27.4121 −0.879697 −0.439849 0.898072i \(-0.644968\pi\)
−0.439849 + 0.898072i \(0.644968\pi\)
\(972\) 13.6844 0.438929
\(973\) −7.50424 −0.240575
\(974\) 10.6164 0.340170
\(975\) 5.01627 0.160649
\(976\) −0.676385 −0.0216506
\(977\) 5.68835 0.181986 0.0909932 0.995852i \(-0.470996\pi\)
0.0909932 + 0.995852i \(0.470996\pi\)
\(978\) 0.181594 0.00580674
\(979\) −2.25504 −0.0720712
\(980\) 1.21967 0.0389609
\(981\) −6.20940 −0.198251
\(982\) −6.29960 −0.201028
\(983\) −52.1324 −1.66276 −0.831382 0.555701i \(-0.812450\pi\)
−0.831382 + 0.555701i \(0.812450\pi\)
\(984\) −20.6222 −0.657412
\(985\) 4.65848 0.148431
\(986\) 26.0470 0.829505
\(987\) −11.8151 −0.376079
\(988\) 1.61048 0.0512361
\(989\) −6.44677 −0.204996
\(990\) 6.35798 0.202070
\(991\) 11.3188 0.359553 0.179777 0.983707i \(-0.442463\pi\)
0.179777 + 0.983707i \(0.442463\pi\)
\(992\) −42.0868 −1.33626
\(993\) 33.1925 1.05333
\(994\) −3.92086 −0.124362
\(995\) 2.75427 0.0873163
\(996\) −36.5651 −1.15861
\(997\) 25.9224 0.820971 0.410485 0.911867i \(-0.365359\pi\)
0.410485 + 0.911867i \(0.365359\pi\)
\(998\) 3.23896 0.102527
\(999\) −39.3933 −1.24635
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))